Figure 3-la shows a simplified rendition of a gear reducer where the input and output shafts AB and CD are rotating at constant speeds and w, respectively. The input and output torques (torsional moments) are T = 240 lbf in and T, respectively. The shafts are supported in the housing by bearings at A, B, C, and D. The pitch radii of gears G, and G2 are ri = 0.75 in and r2 = 1.5 in, respectively. Draw the free-body diagrams of each member and determine the net reaction forces and moments at all points.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.